Erdal Kayacan

Grey system theory-based models in time series prediction

Being able to forecast time series accurately has been quite a popular subject for researchers both in the past and at present. However, the lack of ability of conventional analysis methods to forecast time series that are not smooth leads the scientists and researchers to resort to various forecasting models that have different mathematical backgrounds, such as artificial neural networks, fuzzy predictors, evolutionary and genetic algorithms. In this paper, the accuracies of different grey models such as GM(1,1), Grey Verhulst model, modified grey models using Fourier Series is investigated. Highly noisy data, the United States dollar to Euro parity between the dates 01.01.2005 and 30.12.2007, are used to compare the performances of the different models. The simulation results show that modified grey models have higher performances not only on model fitting but also on forecasting. Among these grey models, the modified GM(1,1) using Fourier series in time is the best in model fitting and forecasting.

A Grey System Modeling Approach for Sliding-Mode Control of Antilock Braking System

In this paper, a grey sliding-mode controller is proposed to regulate the wheel slip, depending on the vehicle forward velocity. The proposed controller anticipates the upcoming values of wheel slip and takes the necessary action to keep the wheel slip at the desired value. The performance of the control algorithm as applied to a quarter vehicle is evaluated through simulations and experimental studies that include sudden changes in road conditions. It is observed that the proposed controller is capable of achieving faster convergence and better noise response than the conventional approaches. It is concluded that the use of grey system theory, which has certain prediction capabilities, can be a viable alternative approach when the conventional control methods cannot meet the desired performance specifications.

Extended Kalman Filter Based Learning Algorithm for Type-2 Fuzzy Logic Systems and Its Experimental Evaluation

In this paper, the use of extended Kalman filter for the optimization of the parameters of type-2 fuzzy logic systems is proposed. The type-2 fuzzy logic system considered in this study benefits from a novel type-2 fuzzy membership function which has certain values on both ends of the support and the kernel, and uncertain values on other parts of the support. To have a comparison of the extended Kalman filter with other existing methods in the literature, particle swarm optimization and gradient descent-based methods are used. The proposed type-2 fuzzy neuro structure is tested on different noisy input-output data sets, and it is shown that extended Kalman filter has a better performance as compared to the gradient descent-based methods. Although the performance of the proposed method is comparable with the particle swarm optimization method, it is faster and more efficient than the particle swarm optimization method. Moreover, the simulation results show that the proposed novel type-2 fuzzy membership function with the extended Kalman filter has noise rejection property. Kalman filter is also used to train the parameters of type-2 fuzzy logic system in a feedback error learning scheme. Then, it is used to control a real-time laboratory setup ABS and satisfactory results are obtained.

Adaptive Neuro-Fuzzy Control of a Spherical Rolling Robot Using Sliding-Mode-Control-Theory-Based Online Learning Algorithm

As a model is only an abstraction of the real system, unmodeled dynamics, parameter variations, and disturbances can result in poor performance of a conventional controller based on this model. In such cases, a conventional controller cannot remain well tuned. This paper presents the control of a spherical rolling robot by using an adaptive neuro-fuzzy controller in combination with a sliding-mode control (SMC)-theory-based learning algorithm. The proposed control structure consists of a neuro-fuzzy network and a conventional controller which is used to guarantee the asymptotic stability of the system in a compact space. The parameter updating rules of the neuro-fuzzy system using SMC theory are derived, and the stability of the learning is proven using a Lyapunov function. The simulation results show that the control scheme with the proposed SMC-theory-based learning algorithm is able to not only eliminate the steady-state error but also improve the transient response performance of the spherical rolling robot without knowing its dynamic equations.

Analysis of the Noise Reduction Property of Type-2 Fuzzy Logic Systems Using a Novel Type-2 Membership Function

In this paper, the noise reduction property of type-2 fuzzy logic (FL) systems (FLSs) (T2FLSs) that use a novel type-2 fuzzy membership function is studied. The proposed type-2 membership function has certain values on both ends of the support and the kernel and some uncertain values for the other values of the support. The parameter tuning rules of a T2FLS that uses such a membership function are derived using the gradient descend learning algorithm. There exist a number of papers in the literature that claim that the performance of T2FLSs is better than type-1 FLSs under noisy conditions, and the claim is tried to be justified by simulation studies only for some specific systems. In this paper, a simpler T2FLS is considered with the novel membership function proposed in which the effect of input noise in the rule base is shown numerically in a general way. The proposed type-2 fuzzy neuro structure is tested on different input-output data sets, and it is shown that the T2FLS with the proposed novel membership function has better noise reduction property when compared to the type-1 counterparts.

A Dynamic Method to Forecast the Wheel Slip for Antilock Braking System and Its Experimental Evaluation

The control of an antilock braking system (ABS) is a difficult problem due to its strongly nonlinear and uncertain characteristics. To overcome this difficulty, the integration of gray-system theory and sliding-mode control is proposed in this paper. This way, the prediction capabilities of the former and the robustness of the latter are combined to regulate optimal wheel slip depending on the vehicle forward velocity. The design approach described is novel, considering that a point, rather than a line, is used as the sliding control surface. The control algorithm is derived and subsequently tested on a quarter vehicle model. Encouraged by the simulation results indicating the ability to overcome the stated difficulties with fast convergence, experimental results are carried out on a laboratory setup. The results presented indicate the potential of the approach in handling difficult real-time control problems.

Sliding Mode Control Approach for Online Learning as Applied to Type-2 Fuzzy Neural Networks and Its Experimental Evaluation

Type-2 fuzzy logic systems (FLSs) are proposed in the literature as an alternative to type-1 FLSs because of their ability to more effectively model uncertainties that may exist in the rule base. However, the parameters of the system still need to be optimized. For this purpose, the use of a sliding mode control theory-based learning algorithm is proposed in this paper. In the approach, instead of trying to minimize an error function, the parameters of the network are tuned by the proposed algorithm in such a way that the learning error is enforced to satisfy a stable equation. The update rules to achieve this are derived, and the convergence of the parameters is proved by Lyapunov stability method. The performance of the proposed algorithm is tested by simulations on a Duffing oscillator and also by real-time experiments on a laboratory servo system. The results indicate that the given type-2 fuzzy neural network with the proposed learning algorithm can handle the uncertainties in a better way as compared to its type-1 counterpart. Moreover, it is computationally easier to implement in real-time systems.

Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm

A neuro-fuzzy adaptive control approach for nonlinear dynamical systems, coupled with unknown dynamics, modeling errors, and various sorts of disturbances, is proposed and used to design a wheel slip regulating controller. The implemented control structure consists of a conventional controller and a neuro-fuzzy network-based feedback controller. The former is provided both to guarantee global asymptotic stability in compact space and as an inverse reference model of the response of the controlled system. Its output is used as an error signal by an incremental learning algorithm to update the parameters of the neuro-fuzzy controller. In this way the latter is able to gradually replace the conventional controller from the control of the system. The proposed new learning algorithm makes direct use of the variable structure systems theory and establishes a sliding motion in terms of the neuro-fuzzy controller parameters, leading the learning error toward zero. In the simulations and in the experimental studies, it has been tested on the control of antilock breaking system model and the analytical claims have been justified under the existence of uncertainty and large nonzero initial errors.

A servo system control with time-varying and nonlinear load conditions using type-2 TSK fuzzy neural system

Abstract: A type-2 Takagi-Sugeno-Kang fuzzy neural system is proposed and its parameter update rules are derived using fuzzy clustering and gradient learning algorithms. The proposed type-2 fuzzy neural system is used for the control and the identification of a real-time servo system. Fuzzy c-means clustering algorithm is used to determine the initial places of the membership functions to ensure that the gradient descent algorithm used afterwards converges in a shorter time. A number of different load conditions including nonlinear and time-varying ones are used to investigate the performance of the proposed control algorithm. The control structure has the ability to regulate the servo system with reduced oscillations when compared with the results of its type-1 counterpart around the set point signal in the presence of load disturbances.

Towards Agrobots: Trajectory Control of an Autonomous Tractor Using Type-2 Fuzzy Logic Controllers

Provision of some autonomous functions to an agricultural vehicle would lighten the job of the operator but in doing so, the accuracy should not be lost to still obtain an optimal yield. Autonomous navigation of an agricultural vehicle involves the control of different dynamic subsystems, such as the yaw angle dynamics and the longitudinal speed dynamics. In this study, a proportional-integral-derivative controller is used to control the longitudinal velocity of the tractor. For the control of the yaw angle dynamics, a proportional-derivative controller works in parallel with a type-2 fuzzy neural network. In such an arrangement, the former ensures the stability of the related subsystem, while the latter learns the system dynamics and becomes the leading controller. In this way, instead of modeling the interactions between the subsystems prior to the design of a model-based control, we develop a control algorithm which learns the interactions online from the measured feedback error. In addition to the control of the stated subsystems, a kinematic controller is needed to correct the errors in both the x- and the y- axis for the trajectory tracking problem of the tractor. To demonstrate the real-time abilities of the proposed control scheme, an autonomous tractor is equipped with the use of reasonably priced sensors and actuators. Experimental results show the efficacy and the efficiency of the proposed learning algorithm.